Draw the following graphs:
y = -x, y = -2x, y = -(1/2)x and y = -(1/3)x.
In the above problems to find y value we can take any value for x, but our
convenience we are taking only integers.

The ordered pairs for the graph y = -x

x

-2

-1

1

2

y = -x

2

1

-1

-2

Ordered pairs

(-2,2)

(-1,1)

(1,-1)

(2,-2)

The ordered pairs for the graph y = -2x

x

-2

-1

1

2

y = -2x

4

2

-2

-4

Ordered pairs

(-2,4)

(-1,2)

(1,-2)

(2,-4)

The ordered pairs for the graph y = -(1/2)x

x

-4

-2

2

4

y = -(1/2)x

2

1

-1

-2

Ordered pairs

(-4,2)

(-2,1)

(2,-1)

(4,-2)

The ordered pairs for the graph y = -(1/3)x

x

-6

-3

3

6

y = -(1/3)x

2

1

-1

-2

Ordered pairs

(-6,2)

(-3,1)

(3,-1)

(6,-2)

Observing above graphs:

1. All these lines are passing through the origin.
2. All these lines are passing through II and IV quadrants.
3. The general form of these lines are y = mx, where m = -1/3, -1/2, -1 and -2.
4. For negative value of m that is the coefficient of x is negative and the graph slopes upwards to left, as the value of m
decreases the line move towards Y-axis.
5. In y = mx, m is known as the slope and m is the coefficient of x.
6. m = y/m, that is slope is the ratio between y-coordinate and x-coordinate.

For any m Î R, y = mx is a straight line and passes through the origin.